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arXiv · 2411.00587

The Stacey-Roberts Lemma for Banach Manifolds

Peter Kristel·Alexander Schmeding
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Abstract

The Stacey-Roberts lemma states that a surjective submersion between finite-dimensional manifolds gives rise to a submersion on infinite-dimensional manifolds of smooth mappings by pushforward. This result is foundational for many constructions in infinite-dimensional differential geometry such as the construction of Lie groupoids of smooth mappings. We generalise the Stacey-Roberts lemma to Banach manifolds which admit smooth partitions of unity.The new approach also remedies an error in the original proof of the result for the purely finite-dimensional setting.

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Peter Kristel, Alexander Schmeding. 2024-11-01. The Stacey-Roberts Lemma for Banach Manifolds. https://doi.org/10.3842/sigma.2025.037

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